scholarly journals Forbidden Substrings, Kolmogorov Complexity and Almost Periodic Sequences

2006 ◽  
pp. 396-407 ◽  
Author(s):  
A. Yu. Rumyantsev ◽  
M. A. Ushakov
Keyword(s):  
Kolmogorov Complexity ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences

scholarly journals Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Zhang ◽  
Bin Jing ◽  
Yingqi Li ◽  
Xiaofeng Fang
Keyword(s):  
Periodic Solution ◽  
Global Analysis ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences ◽  
Globally Attractive ◽  
Mutualism System

This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.

Finite-automaton transformations of strictly almost-periodic sequences

2006 ◽  
Vol 80 (5-6) ◽  
pp. 710-714 ◽  
Author(s):  
Yu. L. Pritykin
Keyword(s):  
Finite Automaton ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences

scholarly journals Sublacunary sets and interpolation sets for nilsequences

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Anh N. Le
Keyword(s):  
Bounded Function ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
New Class ◽  
Finite Set ◽  
Almost Periodic Sequences

<p style='text-indent:20px;'>A set <inline-formula><tex-math id="M1">\begin{document}$ E \subset \mathbb{N} $\end{document}</tex-math></inline-formula> is an interpolation set for nilsequences if every bounded function on <inline-formula><tex-math id="M2">\begin{document}$ E $\end{document}</tex-math></inline-formula> can be extended to a nilsequence on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{N} $\end{document}</tex-math></inline-formula>. Following a theorem of Strzelecki, every lacunary set is an interpolation set for nilsequences. We show that sublacunary sets are not interpolation sets for nilsequences. Here <inline-formula><tex-math id="M4">\begin{document}$ \{r_n: n \in \mathbb{N}\} \subset \mathbb{N} $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M5">\begin{document}$ r_1 &lt; r_2 &lt; \ldots $\end{document}</tex-math></inline-formula> is <i>sublacunary</i> if <inline-formula><tex-math id="M6">\begin{document}$ \lim_{n \to \infty} (\log r_n)/n = 0 $\end{document}</tex-math></inline-formula>. Furthermore, we prove that the union of an interpolation set for nilsequences and a finite set is an interpolation set for nilsequences. Lastly, we provide a new class of interpolation sets for Bohr almost periodic sequences, and as a result, obtain a new example of interpolation set for <inline-formula><tex-math id="M7">\begin{document}$ 2 $\end{document}</tex-math></inline-formula>-step nilsequences which is not an interpolation set for Bohr almost periodic sequences.</p>

Recurrent and almost-periodic sequences

1997 ◽  
Vol 68 (1) ◽  
pp. 22-26 ◽  
Author(s):  
Lutz G. Lucht
Keyword(s):  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences

scholarly journals Rotation sets and almost periodic sequences

2016 ◽  
Vol 284 (1-2) ◽  
pp. 271-284
Author(s):  
T. Jäger ◽  
A. Passeggi ◽  
S. Štimac
Keyword(s):  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences
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